Dynamics of a delayed-feedback oscillator with cubic nonlinearity driven by an external harmonic signal is considered in a case when in the free-running oscillator periodic regime is realized. Resonance curves, i.e. amplitude–frequency responses of the oscillator are derived analytically. Stability conditions for synchronization regime are analyzed. Synchronization tongues on the driving amplitude – driving frequency parameter plane are presented. General differences from classical picture of synchronization of the systems with one degree of freedom are discussed.